In a cooling system of an internal combustion engine for motor vehicles having a fan driven by a viscous coupling (fluid coupling), it is known that the temperature of the cooling system may be regulated in that slippage of the coupling is controlled by a control unit. As the need for cooling increases, the degree of engagement of the coupling, i.e., the ratio of output speed to input speed, increases. However, as this ratio increases, i.e., as slippage is reduced, the time that is required in order to pump the viscous fluid out of the chamber of the coupling, and to reduce the degree of engagement of the coupling to a lower required value, increases. This time lag of the viscosity coupling at a high degree of engagement has the disadvantage that the fan continues to run unnecessarily upon a reduction in the engine load. This continued running results, on the one hand, in disadvantageous cooling of the engine and, on the other, in superfluous consumption of energy and fuel.